The destruction of the Periphery WarShip fleets during the uprising was noted by the author of First Succession War on the Catalyst forums and confirmed by a BattleTech Developer, although not in the Ask The Writers or Ask the Lead Developer forum, so this note is not definitive until confirmed elsewhere:

“

Yup. Only one WarShip operational in ALL of the Periphery. And it was a Concordat boat.

Given the lack of any new WarShips apparently being constructed between the end of the Periphery Uprising in 2766 and the end of the First Succession War in 2821 it is likely, but not certain, that the Periphery nations had also lost the ability to manufacture new WarShips through the destruction or crippling of the relevant shipyards.